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The Rising of the Shield Hero fits. If you're looking for romance you might be somewhat disappointed however. The girl's ten, and the guy treats her more like a daughter than anything else, even after she has the mother of all growth spurts.
Although she's a little ways down the hierarchy, you'll find a catgirl in Issei's harem in High School DxD. You don't find out she's a catgirl for a few seasons though, as her nekomata nature is a very sensitive point for her. That said the name kind of gives it away.
Also, are you only looking for mammal hybrids? Because Dragonar Academy has a rather cute draconic version of this.
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